#We are using a .dat file (survey.dat) created from the SPSS file survey.sav taken from SPSS Survival Manual 6th Edition Julie Pallant
#http://spss.allenandunwin.com.s3-website-ap-southeast-2.amazonaws.com/data-files.html#.Wb0vvnWP-po
#Results on a survey on well being
#We need to load the file so that we can use it in R.
sdata <- read.table("../data/survey.dat")
#Setting the column names to be that used in the dataset
colnames(sdata) <- tolower(colnames(sdata))
#Look first at partial correlation
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
names(sdata)
## [1] "id" "sex" "age" "marital" "child"
## [6] "educ" "source" "smoke" "smokenum" "op1"
## [11] "op2" "op3" "op4" "op5" "op6"
## [16] "mast1" "mast2" "mast3" "mast4" "mast5"
## [21] "mast6" "mast7" "pn1" "pn2" "pn3"
## [26] "pn4" "pn5" "pn6" "pn7" "pn8"
## [31] "pn9" "pn10" "pn11" "pn12" "pn13"
## [36] "pn14" "pn15" "pn16" "pn17" "pn18"
## [41] "pn19" "pn20" "lifsat1" "lifsat2" "lifsat3"
## [46] "lifsat4" "lifsat5" "pss1" "pss2" "pss3"
## [51] "pss4" "pss5" "pss6" "pss7" "pss8"
## [56] "pss9" "pss10" "sest1" "sest2" "sest3"
## [61] "sest4" "sest5" "sest6" "sest7" "sest8"
## [66] "sest9" "sest10" "m1" "m2" "m3"
## [71] "m4" "m5" "m6" "m7" "m8"
## [76] "m9" "m10" "pc1" "pc2" "pc3"
## [81] "pc4" "pc5" "pc6" "pc7" "pc8"
## [86] "pc9" "pc10" "pc11" "pc12" "pc13"
## [91] "pc14" "pc15" "pc16" "pc17" "pc18"
## [96] "rop2" "rop4" "rop6" "rmast1" "rmast3"
## [101] "rmast4" "rmast6" "rmast7" "rpss4" "rpss5"
## [106] "rpss7" "rpss8" "rsest3" "rsest5" "rsest7"
## [111] "rsest9" "rsest10" "rpc1" "rpc2" "rpc7"
## [116] "rpc11" "rpc15" "rpc16" "toptim" "tmast"
## [121] "tposaff" "tnegaff" "tlifesat" "tpstress" "tslfest"
## [126] "tmarlow" "tpcoiss" "agegp3" "agegp5" "educrec"
## [131] "lg10negaff" "mah_1" "coo_1" "mah_2"
ydata<- filter(sdata,!is.na(sdata$tpcoiss), !is.na(sdata$tpstress), !is.na(sdata$toptim),!is.na(sdata$tmarlow))
head(ydata)
## id sex age marital child educ
## 1 415 FEMALES 24 MARRIED FIRST TIME YES COMPLETED UNDERGRADUATE
## 2 9 MALES 39 LIVING WITH PARTNER YES COMPLETED UNDERGRADUATE
## 3 425 FEMALES 48 MARRIED FIRST TIME YES SOME SECONDARY
## 4 307 MALES 41 REMARRIED YES SOME SECONDARY
## 5 440 MALES 23 SINGLE NO COMPLETED UNDERGRADUATE
## 6 484 FEMALES 31 MARRIED FIRST TIME YES COMPLETED UNDERGRADUATE
## source smoke smokenum op1 op2 op3 op4 op5 op6 mast1 mast2 mast3
## 1 LIFE IN GENERAL NO NA 3 2 3 2 4 2 2 4 2
## 2 WORK YES 2 2 3 4 3 5 4 2 4 2
## 3 CHILDREN NO NA 3 1 3 3 3 4 3 3 2
## 4 WORK NO 0 3 1 5 3 5 1 2 4 1
## 5 WORK NO 0 3 2 3 2 1 3 1 4 2
## 6 LIFE IN GENERAL NO NA 2 2 2 2 3 4 1 3 2
## mast4 mast5 mast6 mast7 pn1 pn2 pn3 pn4 pn5 pn6 pn7 pn8 pn9 pn10 pn11
## 1 2 4 2 3 5 5 4 4 4 5 5 5 5 5 5
## 2 3 4 2 3 4 5 4 5 3 3 3 2 5 4 4
## 3 3 3 2 2 2 1 2 2 1 1 3 1 1 1 1
## 4 1 4 1 2 5 5 3 5 2 5 5 5 5 5 5
## 5 1 2 2 2 1 1 1 1 1 1 1 2 3 1 1
## 6 2 3 1 2 2 1 1 3 1 2 1 1 1 1 3
## pn12 pn13 pn14 pn15 pn16 pn17 pn18 pn19 pn20 lifsat1 lifsat2 lifsat3
## 1 5 5 3 5 3 5 5 4 4 5 6 5
## 2 4 4 3 2 2 2 3 4 4 7 6 5
## 3 1 1 2 2 2 1 1 2 1 7 7 7
## 4 5 4 2 5 5 5 5 3 1 7 6 7
## 5 1 1 1 1 1 1 1 1 1 3 3 4
## 6 1 1 1 1 1 1 1 1 1 2 2 2
## lifsat4 lifsat5 pss1 pss2 pss3 pss4 pss5 pss6 pss7 pss8 pss9 pss10 sest1
## 1 4 3 3 3 4 3 4 3 3 3 3 2 4
## 2 7 5 2 2 3 5 4 3 5 4 3 3 3
## 3 6 6 1 2 2 4 4 2 4 4 2 2 4
## 4 7 6 4 3 5 5 4 3 3 4 5 3 4
## 5 3 3 2 2 3 2 3 2 4 3 3 3 2
## 6 2 2 1 1 3 4 3 2 4 3 2 2 2
## sest2 sest3 sest4 sest5 sest6 sest7 sest8 sest9 sest10 m1 m2 m3 m4 m5 m6
## 1 4 1 4 1 4 2 4 3 3 1 0 1 1 0 0
## 2 4 1 4 1 4 3 3 1 3 1 1 1 0 1 0
## 3 3 3 3 1 3 2 3 2 2 1 1 1 1 1 0
## 4 4 1 4 1 4 1 4 1 1 1 1 0 0 0 0
## 5 2 2 2 4 2 3 2 3 2 1 0 1 1 0 0
## 6 3 2 3 2 2 3 2 3 3 1 1 1 1 1 1
## m7 m8 m9 m10 pc1 pc2 pc3 pc4 pc5 pc6 pc7 pc8 pc9 pc10 pc11 pc12 pc13
## 1 1 0 0 0 4 4 3 3 4 4 4 2 3 2 4 4 2
## 2 0 1 0 0 4 3 3 4 3 2 5 1 1 1 5 2 4
## 3 1 1 0 1 3 3 4 2 3 3 3 3 3 3 4 3 2
## 4 0 1 0 0 2 2 4 5 4 4 4 3 4 4 1 3 2
## 5 0 1 0 0 1 2 2 1 2 1 2 2 3 1 3 2 1
## 6 1 1 1 1 1 3 4 3 2 1 4 2 3 3 3 1 4
## pc14 pc15 pc16 pc17 pc18 rop2 rop4 rop6 rmast1 rmast3 rmast4 rmast6
## 1 2 3 3 4 4 4 4 4 3 3 3 3
## 2 2 4 2 2 2 3 3 2 3 3 2 3
## 3 2 4 4 2 2 5 3 2 2 3 2 3
## 4 2 3 2 4 2 5 3 5 3 4 4 4
## 5 3 2 1 1 2 4 4 3 4 3 4 3
## 6 1 4 4 1 1 4 4 2 4 3 3 4
## rmast7 rpss4 rpss5 rpss7 rpss8 rsest3 rsest5 rsest7 rsest9 rsest10 rpc1
## 1 2 3 2 3 3 4 4 3 2 2 2
## 2 2 1 2 1 2 4 4 2 4 2 2
## 3 3 2 2 2 2 2 4 3 3 3 3
## 4 3 1 2 3 2 4 4 4 4 4 4
## 5 3 4 3 2 3 3 1 2 2 3 5
## 6 3 2 3 2 3 3 3 2 2 2 5
## rpc2 rpc7 rpc11 rpc15 rpc16 toptim tmast tposaff tnegaff tlifesat
## 1 2 2 2 3 3 22 22 49 39 23
## 2 3 1 1 2 4 19 21 35 35 30
## 3 3 3 2 2 2 19 19 15 14 33
## 4 4 2 5 3 4 26 26 49 36 33
## 5 4 4 3 4 5 18 23 12 11 16
## 6 3 2 3 2 2 17 23 14 12 10
## tpstress tslfest tmarlow tpcoiss agegp3 agegp5
## 1 29 35 4 51 18 - 29 18 - 24
## 2 22 34 5 40 30 - 44 33 - 40
## 3 19 31 8 47 45+ 41 - 49
## 4 31 40 3 63 30 - 44 41 - 49
## 5 27 21 4 46 18 - 29 18 - 24
## 6 21 24 10 43 30 - 44 25 - 32
## educrec lg10negaff mah_1 coo_1 mah_2
## 1 completed undergrad uni 1.623249 0.9580162 4.534498e-05 18.10064
## 2 completed undergrad uni 1.544068 3.6407533 1.585239e-02 14.48201
## 3 did not complete high school 1.146128 1.3074179 1.404248e-02 14.21429
## 4 did not complete high school 1.556303 1.3141761 5.403849e-03 14.16941
## 5 completed undergrad uni 1.041393 2.7188874 3.755638e-04 13.70297
## 6 completed undergrad uni 1.079181 3.7542989 1.351416e-02 13.56551
library(ppcor)
## Loading required package: MASS
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
#perception of control and stress controlling for social desirability
spcor.test(ydata$tpcoiss, ydata$tpstress, ydata$tmarlow)
## estimate p.value statistic n gp Method
## 1 -0.5269534 1.862222e-31 -12.69154 422 1 pearson
#perception of control and optimism controlling for social desirability
spcor.test(ydata$tpcoiss, ydata$toptim, ydata$tmarlow)
## estimate p.value statistic n gp Method
## 1 0.4830465 5.348979e-26 11.29257 422 1 pearson
#stress and optimism controlling for social desirability
spcor.test(ydata$tpstress, ydata$toptim, ydata$tmarlow)
## estimate p.value statistic n gp Method
## 1 -0.4412444 1.73877e-21 -10.06483 422 1 pearson
#Look at differences in scores for gender
#Conduct Levene's test for homogeneity of variance in library car
library(car)
## Loading required package: carData
##
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
##
## recode
leveneTest(tpstress ~ sex, data=ydata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 1.678 0.1959
## 420
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(tpstress~sex,var.equal=FALSE,data=ydata)#Variances are not equal
##
## Welch Two Sample t-test
##
## data: tpstress by sex
## t = 3.0956, df = 402.98, p-value = 0.002101
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.635108 2.845362
## sample estimates:
## mean in group FEMALES mean in group MALES
## 27.46091 25.72067
#Conduct Levene's test for homogeneity of variance in library car
leveneTest(tpcoiss ~ sex, data=ydata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 2.2499 0.1344
## 420
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(tpcoiss~sex,var.equal=FALSE,data=ydata)
##
## Welch Two Sample t-test
##
## data: tpcoiss by sex
## t = -2.1841, df = 401.99, p-value = 0.02953
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -4.8177980 -0.2533563
## sample estimates:
## mean in group FEMALES mean in group MALES
## 59.49794 62.03352
#Conduct Levene's test for homogeneity of variance in library car
leveneTest(toptim ~ sex, data=ydata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 4.5018 0.03444 *
## 420
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(toptim~sex,var.equal=TRUE,data=ydata)
##
## Two Sample t-test
##
## data: toptim by sex
## t = 0.40731, df = 420, p-value = 0.684
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.6780665 1.0325278
## sample estimates:
## mean in group FEMALES mean in group MALES
## 22.23868 22.06145
#Conduct Levene's test for homogeneity of variance in library car
leveneTest(tmarlow ~ sex, data=sdata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.0132 0.9087
## 431
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(tmarlow~sex,var.equal=FALSE,data=ydata)
##
## Welch Two Sample t-test
##
## data: tmarlow by sex
## t = 1.9176, df = 388.54, p-value = 0.05589
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.009565282 0.766720947
## sample estimates:
## mean in group FEMALES mean in group MALES
## 5.456790 5.078212
#install the library userfriendlyscience and load it using the library command
#it has a really nice one-way anova function that provides
#nice summary output
library(userfriendlyscience)
#run a one-way anova test using the correct post-hoc test Tukey in our case
#Use Games-Howell for unequal variances
one.way <- oneway(ydata$agegp3, y = ydata$toptim, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=toptim and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [0; .06], point estimate = .02
## Eta Squared: 95% CI = [0; .05], point estimate = .02
##
## SS Df MS F p
## Between groups (error + effect) 196.06 2 98.03 5.13 .006
## Within groups (error only) 8003.66 419 19.1
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 0.66 -0.54 1.86 .403
## 45+-18 - 29 1.69 0.44 2.94 .004
## 45+-30 - 44 1.04 -0.2 2.27 .121
one.way <- oneway(ydata$agegp3, y = ydata$tpstress, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=tpstress and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [NA; .04], point estimate = .01
## Eta Squared: 95% CI = [0; .03], point estimate = .01
##
## SS Df MS F p
## Between groups (error + effect) 160.54 2 80.27 2.36 .096
## Within groups (error only) 14262.02 419 34.04
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 -1.01 -2.61 0.59 .301
## 45+-18 - 29 -1.5 -3.16 0.17 .089
## 45+-30 - 44 -0.49 -2.14 1.16 .767
one.way <- oneway(ydata$agegp3, y = ydata$tpcoiss, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=tpcoiss and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [.01; .08], point estimate = .04
## Eta Squared: 95% CI = [.01; .08], point estimate = .04
##
## SS Df MS F p
## Between groups (error + effect) 2626.31 2 1313.16 9.47 <.001
## Within groups (error only) 58102.91 419 138.67
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 1.34 -1.89 4.57 .592
## 45+-18 - 29 5.97 2.61 9.34 <.001
## 45+-30 - 44 4.63 1.3 7.96 .003
one.way <- oneway(ydata$agegp3, y = ydata$tmarlow, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=tmarlow and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [.02; .1], point estimate = .05
## Eta Squared: 95% CI = [.02; .09], point estimate = .06
##
## SS Df MS F p
## Between groups (error + effect) 95.21 2 47.61 12.32 <.001
## Within groups (error only) 1618.76 419 3.86
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 0.79 0.25 1.33 .002
## 45+-18 - 29 1.15 0.58 1.71 <.001
## 45+-30 - 44 0.35 -0.2 0.91 .297
Build the linear regression models
#Baseline model optimism and social desirability as predictors
model1=lm(ydata$tpcoiss~ydata$toptim+ydata$tmarlow)
summary(model1)
##
## Call:
## lm(formula = ydata$tpcoiss ~ ydata$toptim + ydata$tmarlow)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.5175 -6.4859 0.4332 6.4263 26.2576
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.7960 2.6606 8.944 < 2e-16 ***
## ydata$toptim 1.3249 0.1104 11.998 < 2e-16 ***
## ydata$tmarlow 1.3996 0.2415 5.795 1.35e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.921 on 419 degrees of freedom
## Multiple R-squared: 0.3209, Adjusted R-squared: 0.3176
## F-statistic: 98.98 on 2 and 419 DF, p-value: < 2.2e-16
plot(model1)
#Check assumptions
#Cooks distance
cooks.distance(model1)
## 1 2 3 4 5
## 6.506115e-04 3.129057e-03 5.087877e-03 8.452198e-06 9.240629e-04
## 6 7 8 9 10
## 2.161413e-02 2.048926e-02 1.193240e-02 1.939681e-02 3.356655e-02
## 11 12 13 14 15
## 2.146690e-02 1.566864e-02 1.287334e-09 1.277584e-02 2.627391e-03
## 16 17 18 19 20
## 4.739549e-03 5.190616e-03 9.023535e-04 5.028507e-03 9.223243e-04
## 21 22 23 24 25
## 5.089454e-04 8.069809e-03 9.064434e-04 6.878265e-04 2.129152e-03
## 26 27 28 29 30
## 6.964412e-04 4.149586e-03 1.524208e-04 5.381614e-04 1.224734e-03
## 31 32 33 34 35
## 5.821577e-02 2.108022e-04 4.576823e-05 7.420428e-05 1.952397e-03
## 36 37 38 39 40
## 6.069657e-04 1.150524e-03 9.023535e-04 2.875893e-04 8.964110e-03
## 41 42 43 44 45
## 2.513665e-03 4.173919e-03 1.593331e-03 3.366332e-04 2.249850e-03
## 46 47 48 49 50
## 2.567601e-04 4.621626e-06 5.983472e-05 2.968610e-04 4.357802e-03
## 51 52 53 54 55
## 7.879206e-03 8.223513e-03 2.919133e-04 1.551056e-04 2.820941e-03
## 56 57 58 59 60
## 2.721381e-05 7.439357e-03 1.214220e-03 2.455651e-04 1.955042e-02
## 61 62 63 64 65
## 8.217066e-03 2.531394e-02 2.938392e-05 3.485609e-03 5.595200e-04
## 66 67 68 69 70
## 3.067932e-03 1.221729e-04 3.111358e-04 4.399424e-04 1.178932e-03
## 71 72 73 74 75
## 1.153362e-03 6.837250e-06 6.168852e-03 4.165562e-03 6.094952e-04
## 76 77 78 79 80
## 1.845418e-02 2.968610e-04 2.848670e-04 6.064830e-04 2.401268e-03
## 81 82 83 84 85
## 9.691870e-04 6.827054e-04 1.021566e-03 1.001439e-04 3.270077e-04
## 86 87 88 89 90
## 1.723499e-03 9.107545e-07 6.971367e-03 9.013481e-04 1.658224e-04
## 91 92 93 94 95
## 1.402775e-03 4.077905e-03 6.812020e-04 7.180430e-03 8.656207e-05
## 96 97 98 99 100
## 6.582227e-05 4.193576e-05 3.458286e-03 3.127371e-05 2.264226e-04
## 101 102 103 104 105
## 1.392142e-03 1.354924e-03 2.522240e-05 2.631634e-03 1.063894e-06
## 106 107 108 109 110
## 1.924593e-03 1.060526e-02 8.806716e-05 3.650248e-03 5.889678e-05
## 111 112 113 114 115
## 3.010354e-05 5.381614e-04 3.067745e-04 8.517758e-03 2.963168e-03
## 116 117 118 119 120
## 1.176251e-03 2.936065e-04 1.650252e-03 1.656681e-03 3.342240e-05
## 121 122 123 124 125
## 2.066646e-03 4.975720e-03 6.012884e-03 1.763650e-05 1.274406e-04
## 126 127 128 129 130
## 1.487809e-04 4.591151e-05 2.235437e-03 1.025210e-04 1.402666e-03
## 131 132 133 134 135
## 1.513572e-03 2.295381e-04 4.692662e-03 5.194474e-03 1.632979e-03
## 136 137 138 139 140
## 1.624723e-04 1.198991e-04 3.583611e-03 4.056554e-04 3.335224e-04
## 141 142 143 144 145
## 3.797979e-05 4.819077e-03 2.773353e-03 1.499621e-04 5.689831e-05
## 146 147 148 149 150
## 2.862607e-03 9.999551e-03 4.909010e-03 7.464769e-04 9.777531e-05
## 151 152 153 154 155
## 4.087176e-03 3.036948e-05 1.757349e-04 7.157722e-04 4.139358e-04
## 156 157 158 159 160
## 3.495057e-03 1.924870e-06 1.350806e-06 3.964415e-04 1.039854e-06
## 161 162 163 164 165
## 1.091038e-03 1.372123e-04 3.445105e-04 2.179824e-03 1.175263e-03
## 166 167 168 169 170
## 6.338430e-03 9.987183e-05 7.884016e-04 2.073466e-03 1.554853e-04
## 171 172 173 174 175
## 1.198991e-04 4.994177e-03 1.380328e-03 4.696045e-03 2.464019e-03
## 176 177 178 179 180
## 5.179151e-03 3.382006e-03 1.468342e-07 6.529841e-03 1.144402e-02
## 181 182 183 184 185
## 5.708992e-03 6.957986e-03 8.605417e-05 4.538805e-04 1.210417e-03
## 186 187 188 189 190
## 1.170647e-03 1.397110e-03 2.642224e-03 3.434621e-06 1.053473e-04
## 191 192 193 194 195
## 6.040439e-03 1.021492e-05 2.621312e-05 3.058127e-04 1.106836e-06
## 196 197 198 199 200
## 3.084810e-04 3.681709e-04 7.158949e-06 7.232093e-04 5.107740e-05
## 201 202 203 204 205
## 1.677699e-04 5.885062e-04 2.053106e-04 7.578335e-04 4.736659e-04
## 206 207 208 209 210
## 4.538805e-04 1.919009e-02 5.959021e-06 1.174626e-03 3.559009e-04
## 211 212 213 214 215
## 1.179592e-07 2.617542e-03 1.439938e-03 5.375908e-04 6.156527e-03
## 216 217 218 219 220
## 1.949562e-04 2.161649e-04 3.375625e-04 2.521972e-03 3.342415e-04
## 221 222 223 224 225
## 9.711773e-05 1.052173e-03 2.070093e-03 1.642951e-03 1.752558e-04
## 226 227 228 229 230
## 2.359908e-04 1.380037e-05 5.696251e-04 2.503399e-05 3.978605e-03
## 231 232 233 234 235
## 3.412849e-03 7.974683e-03 7.578335e-04 4.340043e-06 4.957295e-05
## 236 237 238 239 240
## 1.072370e-04 1.524910e-03 3.167750e-08 7.816887e-04 3.989980e-04
## 241 242 243 244 245
## 4.328349e-03 1.195432e-03 2.627620e-02 5.271424e-03 5.104507e-03
## 246 247 248 249 250
## 2.922495e-03 9.186979e-03 4.017850e-04 1.271078e-03 6.135397e-07
## 251 252 253 254 255
## 8.145769e-04 1.688660e-03 7.337091e-05 3.999015e-05 1.078057e-04
## 256 257 258 259 260
## 6.388485e-04 3.409956e-04 4.957295e-05 1.792341e-04 3.701106e-04
## 261 262 263 264 265
## 8.368294e-05 2.935490e-03 7.674842e-03 1.131683e-03 1.280714e-04
## 266 267 268 269 270
## 5.598536e-05 2.223945e-03 4.416331e-03 1.857985e-03 1.672161e-02
## 271 272 273 274 275
## 6.659797e-03 2.483211e-05 1.966412e-03 1.061073e-04 1.129694e-03
## 276 277 278 279 280
## 8.682361e-03 6.418422e-05 7.193885e-03 3.001158e-03 3.342110e-04
## 281 282 283 284 285
## 1.372123e-04 4.290792e-03 8.865922e-06 1.651619e-03 2.033704e-04
## 286 287 288 289 290
## 5.499787e-04 7.280757e-04 1.439891e-03 2.904122e-04 1.256372e-03
## 291 292 293 294 295
## 1.294287e-03 2.284546e-03 2.700759e-02 1.490000e-03 4.149014e-04
## 296 297 298 299 300
## 3.109561e-03 4.616497e-04 9.050319e-06 4.594888e-07 7.625216e-03
## 301 302 303 304 305
## 2.566532e-03 1.649468e-03 6.496286e-06 1.914557e-05 2.785114e-03
## 306 307 308 309 310
## 4.364782e-04 1.757705e-03 2.343748e-03 2.867822e-03 4.054453e-06
## 311 312 313 314 315
## 9.264442e-04 1.746174e-03 1.452083e-03 9.805261e-04 1.584094e-05
## 316 317 318 319 320
## 1.008374e-04 1.256380e-05 3.010354e-05 4.532669e-04 5.594561e-04
## 321 322 323 324 325
## 1.823669e-03 1.941765e-05 2.936065e-04 8.714722e-05 6.589561e-04
## 326 327 328 329 330
## 7.834848e-03 2.967029e-05 1.210417e-03 3.524980e-03 1.711533e-03
## 331 332 333 334 335
## 7.967586e-04 9.576450e-04 6.905434e-05 6.421580e-05 1.571377e-04
## 336 337 338 339 340
## 4.793292e-05 8.724819e-04 3.883082e-04 1.658224e-04 7.986904e-03
## 341 342 343 344 345
## 6.088274e-04 8.053373e-04 2.427713e-03 2.391558e-03 2.106339e-03
## 346 347 348 349 350
## 1.716402e-04 2.674903e-03 1.605706e-04 2.612864e-03 1.126339e-04
## 351 352 353 354 355
## 3.366332e-04 1.137714e-04 1.818245e-04 6.503035e-04 9.047490e-03
## 356 357 358 359 360
## 7.790803e-04 8.288269e-04 9.748803e-05 6.492991e-07 1.508200e-03
## 361 362 363 364 365
## 5.473312e-04 6.387701e-03 3.991669e-03 1.119548e-03 1.642899e-03
## 366 367 368 369 370
## 1.519985e-02 1.620073e-05 1.062820e-03 1.780379e-04 2.819749e-03
## 371 372 373 374 375
## 1.501189e-03 3.294622e-04 9.732599e-06 3.213351e-03 3.193184e-03
## 376 377 378 379 380
## 3.661866e-04 1.492295e-03 6.734092e-04 1.018918e-06 1.862339e-04
## 381 382 383 384 385
## 3.255562e-03 8.866627e-06 4.400965e-03 8.037937e-04 5.023406e-05
## 386 387 388 389 390
## 1.319660e-02 1.553321e-03 4.840320e-04 1.572066e-03 6.204326e-05
## 391 392 393 394 395
## 1.231578e-04 7.545399e-05 1.878922e-03 1.025210e-04 1.466992e-03
## 396 397 398 399 400
## 3.367960e-06 5.141552e-05 2.602819e-03 2.461654e-03 3.410122e-05
## 401 402 403 404 405
## 5.132774e-04 4.397996e-05 7.133846e-05 8.613094e-03 2.990435e-03
## 406 407 408 409 410
## 5.617803e-04 2.694865e-07 1.408026e-03 1.080433e-02 1.438883e-03
## 411 412 413 414 415
## 4.256345e-05 1.779525e-02 1.242404e-03 3.588363e-04 1.279044e-06
## 416 417 418 419 420
## 1.117406e-04 3.575873e-04 2.949043e-04 4.768409e-04 7.689343e-04
## 421 422
## 4.591151e-05 4.500562e-05
#Create histogram
#A density plot of the residuals
plot(density(resid(model1)))
#Create a QQ plot qqPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model1) # leverage plots
#Collinearity
vif(model1)
## ydata$toptim ydata$tmarlow
## 1.015801 1.015801
sqrt(vif(model1))
## ydata$toptim ydata$tmarlow
## 1.00787 1.00787
#Second model adding in stress
model2=lm(ydata$tpcoiss~ydata$toptim+ydata$tmarlow+ydata$tpstress)
summary(model2)
##
## Call:
## lm(formula = ydata$tpcoiss ~ ydata$toptim + ydata$tmarlow + ydata$tpstress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.253 -5.034 0.271 5.701 28.070
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 58.55471 4.40587 13.290 < 2e-16 ***
## ydata$toptim 0.84267 0.11264 7.481 4.38e-13 ***
## ydata$tmarlow 0.98044 0.22400 4.377 1.52e-05 ***
## ydata$tpstress -0.81767 0.08663 -9.438 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.019 on 418 degrees of freedom
## Multiple R-squared: 0.4402, Adjusted R-squared: 0.4361
## F-statistic: 109.5 on 3 and 418 DF, p-value: < 2.2e-16
plot(model2)
#Check assumptions
#Cooks distance
cooks.distance(model2)
## 1 2 3 4 5
## 4.386133e-04 1.122128e-02 1.841839e-02 8.104241e-04 1.677983e-03
## 6 7 8 9 10
## 3.951943e-02 1.278646e-02 1.858489e-02 1.124209e-02 1.319163e-02
## 11 12 13 14 15
## 2.095067e-02 3.536274e-02 2.078877e-04 1.510310e-02 4.006136e-04
## 16 17 18 19 20
## 2.818643e-03 5.081900e-03 2.784382e-02 6.187649e-04 9.385656e-04
## 21 22 23 24 25
## 1.692352e-04 2.913993e-02 2.425825e-03 1.963788e-03 1.334735e-03
## 26 27 28 29 30
## 2.386220e-05 5.446850e-03 1.513688e-03 9.679650e-07 3.836379e-04
## 31 32 33 34 35
## 3.596554e-02 6.542349e-04 1.963583e-04 4.635160e-04 1.006445e-03
## 36 37 38 39 40
## 3.779544e-04 6.207859e-04 2.893225e-03 1.518792e-03 6.252466e-03
## 41 42 43 44 45
## 4.803713e-04 3.623659e-03 1.038313e-02 2.437726e-03 5.997050e-04
## 46 47 48 49 50
## 6.230510e-03 1.268997e-04 1.895822e-03 1.023493e-03 5.358517e-03
## 51 52 53 54 55
## 6.697990e-02 4.617651e-02 7.650889e-04 4.571700e-03 3.066488e-03
## 56 57 58 59 60
## 3.898795e-04 6.702801e-03 9.716547e-04 8.870216e-05 7.531584e-03
## 61 62 63 64 65
## 1.070167e-02 1.516978e-02 5.397230e-05 4.659988e-04 8.643770e-03
## 66 67 68 69 70
## 1.326955e-03 4.032575e-03 7.038843e-04 6.651905e-04 3.143702e-04
## 71 72 73 74 75
## 4.152421e-04 1.621811e-05 7.732975e-04 1.689876e-02 1.567265e-05
## 76 77 78 79 80
## 1.402302e-02 6.050244e-04 3.492398e-04 5.618475e-04 1.600254e-03
## 81 82 83 84 85
## 3.831070e-06 3.579970e-04 3.061522e-04 1.108126e-03 1.156157e-03
## 86 87 88 89 90
## 1.376175e-03 3.209951e-04 3.646189e-03 2.361536e-04 3.462976e-04
## 91 92 93 94 95
## 8.202307e-05 1.680604e-04 7.306675e-04 4.747362e-03 7.856356e-05
## 96 97 98 99 100
## 1.008669e-05 6.809411e-04 1.238707e-02 2.383199e-04 6.062445e-04
## 101 102 103 104 105
## 1.233405e-03 8.383219e-04 2.944082e-04 4.329760e-04 1.011100e-03
## 106 107 108 109 110
## 1.938113e-03 7.450220e-03 1.025415e-04 2.037185e-03 1.223689e-04
## 111 112 113 114 115
## 5.507892e-06 3.817765e-04 3.338964e-05 7.695163e-03 2.624638e-03
## 116 117 118 119 120
## 9.518047e-04 6.441381e-05 1.690502e-03 1.098883e-03 6.995576e-04
## 121 122 123 124 125
## 5.990789e-03 1.280055e-02 3.799758e-03 6.759402e-05 6.630600e-05
## 126 127 128 129 130
## 2.479354e-04 3.051437e-05 5.508596e-04 1.585305e-04 1.050701e-03
## 131 132 133 134 135
## 7.095943e-04 8.935817e-04 6.350803e-04 4.076625e-02 1.429977e-02
## 136 137 138 139 140
## 1.206158e-03 5.763347e-04 2.135666e-03 8.705416e-09 1.884086e-03
## 141 142 143 144 145
## 4.320267e-05 3.078351e-03 2.194644e-03 1.164725e-05 6.621026e-05
## 146 147 148 149 150
## 1.402424e-02 6.955861e-03 3.331298e-03 1.002329e-03 1.530437e-04
## 151 152 153 154 155
## 2.578946e-03 7.411840e-06 4.302432e-04 3.132903e-03 5.284563e-05
## 156 157 158 159 160
## 1.908219e-03 1.067378e-03 5.755838e-04 6.092257e-04 5.196341e-05
## 161 162 163 164 165
## 8.455585e-04 3.543527e-04 1.318425e-04 1.881276e-03 9.157110e-04
## 166 167 168 169 170
## 6.946290e-03 5.300279e-05 2.127500e-05 1.295259e-03 7.237538e-05
## 171 172 173 174 175
## 8.855640e-05 4.740295e-03 1.064043e-03 3.319243e-03 3.817172e-04
## 176 177 178 179 180
## 4.436219e-03 2.669174e-03 9.347653e-04 6.462383e-03 1.053434e-02
## 181 182 183 184 185
## 5.679416e-03 4.930282e-03 4.027091e-04 4.504617e-04 1.643329e-03
## 186 187 188 189 190
## 4.818361e-05 1.592021e-03 2.571586e-03 4.890655e-05 2.127256e-03
## 191 192 193 194 195
## 6.103995e-03 1.201321e-04 1.864803e-04 6.200510e-05 1.986242e-04
## 196 197 198 199 200
## 2.126468e-04 1.579025e-05 2.576602e-05 2.475584e-04 1.012185e-04
## 201 202 203 204 205
## 8.324393e-05 1.107312e-03 3.054095e-07 2.217814e-04 4.681305e-04
## 206 207 208 209 210
## 1.115400e-03 1.223851e-02 5.757810e-06 4.472341e-04 8.394730e-04
## 211 212 213 214 215
## 9.312336e-06 3.066385e-03 4.856027e-04 5.113950e-04 4.688919e-03
## 216 217 218 219 220
## 8.904989e-04 2.971711e-04 1.265362e-04 2.381366e-03 4.750834e-06
## 221 222 223 224 225
## 2.481636e-04 1.304818e-04 1.020656e-03 1.199490e-02 2.910689e-04
## 226 227 228 229 230
## 1.204419e-04 7.463380e-06 7.239221e-04 1.370971e-05 3.586538e-03
## 231 232 233 234 235
## 1.352064e-03 7.742845e-03 3.192741e-05 9.414624e-06 1.400134e-05
## 236 237 238 239 240
## 2.247768e-04 2.751394e-03 4.638816e-06 1.092434e-03 4.336220e-05
## 241 242 243 244 245
## 5.012996e-03 1.846043e-03 2.276583e-02 3.502830e-03 3.373733e-03
## 246 247 248 249 250
## 1.637806e-03 7.437340e-03 6.446441e-05 1.249926e-03 1.628093e-05
## 251 252 253 254 255
## 2.089036e-03 8.269490e-04 6.272452e-04 1.555396e-04 5.870607e-05
## 256 257 258 259 260
## 1.277570e-03 8.920941e-05 1.653760e-03 5.820557e-06 2.716542e-04
## 261 262 263 264 265
## 2.781698e-05 2.372743e-03 7.082099e-03 9.568469e-04 5.097000e-06
## 266 267 268 269 270
## 2.253401e-04 1.783613e-03 3.420871e-03 1.023987e-03 9.543107e-03
## 271 272 273 274 275
## 8.586335e-03 1.260799e-05 4.736527e-03 1.722811e-07 5.328438e-05
## 276 277 278 279 280
## 9.064871e-03 2.146134e-05 5.317210e-03 1.760873e-03 1.905966e-05
## 281 282 283 284 285
## 4.640265e-05 4.380822e-03 1.093820e-04 9.877358e-04 1.344988e-04
## 286 287 288 289 290
## 1.585704e-04 3.916155e-04 7.051611e-04 1.610758e-04 4.548479e-04
## 291 292 293 294 295
## 4.538674e-04 1.201836e-03 2.143479e-02 1.205541e-03 3.031590e-04
## 296 297 298 299 300
## 8.962552e-04 1.114583e-04 1.393493e-04 5.159693e-06 6.983783e-03
## 301 302 303 304 305
## 2.251318e-03 2.902743e-03 2.288025e-04 6.227432e-04 2.346624e-03
## 306 307 308 309 310
## 4.089628e-05 1.387249e-03 2.760761e-03 2.495428e-03 3.530648e-05
## 311 312 313 314 315
## 3.380011e-04 5.835935e-04 2.496055e-03 2.774031e-04 2.308443e-04
## 316 317 318 319 320
## 1.686315e-04 1.143373e-03 9.677548e-05 1.683532e-03 7.132650e-04
## 321 322 323 324 325
## 1.353526e-03 5.250248e-06 1.256242e-04 7.959785e-05 4.593538e-04
## 326 327 328 329 330
## 5.517579e-03 1.932397e-05 5.013628e-04 3.298492e-03 6.990907e-04
## 331 332 333 334 335
## 4.655428e-05 3.522176e-04 2.364236e-05 2.207084e-05 3.881046e-05
## 336 337 338 339 340
## 1.627580e-05 1.514174e-03 1.055266e-04 1.433574e-04 6.123495e-03
## 341 342 343 344 345
## 2.574264e-04 3.304918e-04 6.589807e-04 8.551661e-04 1.323455e-03
## 346 347 348 349 350
## 5.606057e-06 2.238127e-03 5.255332e-05 1.280023e-03 1.999500e-05
## 351 352 353 354 355
## 5.766521e-05 6.914136e-05 6.995432e-05 6.633236e-04 2.361188e-02
## 356 357 358 359 360
## 4.722831e-04 5.031333e-03 2.895058e-04 1.072320e-04 1.141158e-03
## 361 362 363 364 365
## 4.935098e-04 4.322763e-03 4.292238e-03 5.731036e-04 1.015266e-03
## 366 367 368 369 370
## 1.222428e-02 4.520365e-04 8.836257e-04 4.301008e-06 1.025994e-03
## 371 372 373 374 375
## 1.155738e-03 7.250348e-05 6.368504e-04 2.767466e-03 2.247564e-03
## 376 377 378 379 380
## 1.409342e-04 8.629613e-05 3.288017e-06 1.437695e-05 1.175090e-06
## 381 382 383 384 385
## 2.532978e-03 7.736559e-05 4.522563e-03 9.199994e-04 1.636145e-09
## 386 387 388 389 390
## 9.179859e-03 1.939028e-03 1.048373e-03 2.006180e-03 9.043328e-05
## 391 392 393 394 395
## 2.043244e-04 1.819969e-04 5.282918e-03 1.047493e-05 3.865099e-04
## 396 397 398 399 400
## 1.595736e-04 9.715567e-07 1.649315e-03 4.660351e-04 2.702553e-06
## 401 402 403 404 405
## 3.265448e-04 2.975850e-05 1.782046e-04 6.869838e-03 1.578350e-03
## 406 407 408 409 410
## 1.320362e-03 6.239612e-05 3.516138e-03 6.107803e-03 5.268216e-03
## 411 412 413 414 415
## 8.229372e-06 1.461833e-02 9.274811e-04 1.289364e-05 2.072355e-05
## 416 417 418 419 420
## 2.455461e-05 3.639891e-04 2.562616e-04 2.381704e-04 5.211356e-04
## 421 422
## 3.704604e-04 1.143229e-03
#Create histogram
#A density plot of the residuals
plot(density(resid(model2)))
#Create a QQ plot qPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model2) # leverage plots
#Collinearity
vif(model2)
## ydata$toptim ydata$tmarlow ydata$tpstress
## 1.279007 1.057358 1.330851
sqrt(vif(model2))
## ydata$toptim ydata$tmarlow ydata$tpstress
## 1.130932 1.028279 1.153625
#Model 3 adding in gender
#dummycode
ydata$gender=recode(ydata$sex,'0=1;1=2')
model3=lm(ydata$tpcoiss~ydata$toptim+ydata$tmarlow+ydata$tpstress+ydata$gender)
summary(model3)
##
## Call:
## lm(formula = ydata$tpcoiss ~ ydata$toptim + ydata$tmarlow + ydata$tpstress +
## ydata$gender)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.785 -5.241 0.139 5.801 28.424
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 56.17192 4.56967 12.292 < 2e-16 ***
## ydata$toptim 0.86391 0.11285 7.655 1.36e-13 ***
## ydata$tmarlow 1.03612 0.22525 4.600 5.62e-06 ***
## ydata$tpstress -0.78439 0.08814 -8.899 < 2e-16 ***
## ydata$genderMALES 1.71591 0.90775 1.890 0.0594 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.991 on 417 degrees of freedom
## Multiple R-squared: 0.4449, Adjusted R-squared: 0.4396
## F-statistic: 83.56 on 4 and 417 DF, p-value: < 2.2e-16
plot(model3)
#Check assumptions
#Cooks distance
cooks.distance(model3)
## 1 2 3 4 5
## 4.197679e-04 1.211857e-02 1.618401e-02 5.551629e-04 2.264980e-03
## 6 7 8 9 10
## 3.231304e-02 9.922411e-03 2.344161e-02 8.680495e-03 1.496076e-02
## 11 12 13 14 15
## 2.101761e-02 3.420758e-02 9.772502e-05 1.183614e-02 2.118482e-04
## 16 17 18 19 20
## 2.169598e-03 3.911430e-03 2.351318e-02 3.793327e-04 8.606866e-04
## 21 22 23 24 25
## 2.142289e-05 2.556939e-02 2.569283e-03 2.011169e-03 1.843008e-03
## 26 27 28 29 30
## 3.790730e-06 4.373871e-03 1.705208e-03 6.581347e-06 8.048003e-04
## 31 32 33 34 35
## 2.820298e-02 7.733624e-04 8.887682e-05 3.814116e-04 1.321204e-03
## 36 37 38 39 40
## 3.742400e-04 8.454544e-04 3.412412e-03 9.610690e-04 4.561408e-03
## 41 42 43 44 45
## 3.149815e-04 2.948345e-03 9.000356e-03 1.945060e-03 3.657561e-04
## 46 47 48 49 50
## 5.664595e-03 2.798421e-04 1.735660e-03 6.136839e-04 5.376345e-03
## 51 52 53 54 55
## 5.875351e-02 4.307659e-02 8.650980e-04 4.020425e-03 2.287152e-03
## 56 57 58 59 60
## 2.855970e-04 6.774712e-03 9.272567e-04 1.290323e-04 5.768160e-03
## 61 62 63 64 65
## 8.400061e-03 1.183437e-02 3.194868e-05 7.653155e-04 7.403000e-03
## 66 67 68 69 70
## 9.829533e-04 3.375666e-03 9.262198e-04 6.846940e-04 7.718024e-04
## 71 72 73 74 75
## 2.564665e-04 4.014454e-07 6.411572e-04 1.537949e-02 1.245155e-06
## 76 77 78 79 80
## 1.015045e-02 7.780475e-04 3.362903e-04 8.177173e-04 2.374995e-03
## 81 82 83 84 85
## 3.319909e-05 7.542612e-04 1.770498e-04 1.066118e-03 1.332752e-03
## 86 87 88 89 90
## 1.432210e-03 1.959148e-04 4.195844e-03 6.321568e-04 5.037242e-04
## 91 92 93 94 95
## 2.854249e-05 2.739247e-05 8.179369e-04 7.255416e-03 1.756023e-04
## 96 97 98 99 100
## 3.001939e-05 7.345742e-04 1.164994e-02 4.180816e-04 8.294681e-04
## 101 102 103 104 105
## 1.951387e-03 1.144373e-03 4.222578e-04 2.941887e-04 1.290234e-03
## 106 107 108 109 110
## 2.272432e-03 8.906600e-03 3.313974e-05 2.603343e-03 1.867603e-04
## 111 112 113 114 115
## 6.797506e-06 6.601685e-04 1.803555e-07 6.741639e-03 3.422203e-03
## 116 117 118 119 120
## 1.503357e-03 1.788088e-05 2.180131e-03 1.285808e-03 9.625718e-04
## 121 122 123 124 125
## 4.953154e-03 1.233853e-02 2.830108e-03 1.493332e-05 1.607792e-06
## 126 127 128 129 130
## 1.364789e-04 1.130918e-04 3.546110e-04 1.718545e-04 1.339119e-03
## 131 132 133 134 135
## 1.268833e-03 1.004576e-03 3.598073e-04 3.457427e-02 1.177440e-02
## 136 137 138 139 140
## 1.465423e-03 6.586219e-04 1.692150e-03 5.728757e-06 1.557841e-03
## 141 142 143 144 145
## 1.118464e-05 3.838866e-03 3.106583e-03 8.568775e-05 3.553826e-05
## 146 147 148 149 150
## 1.246649e-02 8.086788e-03 2.643602e-03 1.456764e-03 3.460046e-04
## 151 152 153 154 155
## 1.996944e-03 1.239686e-06 5.470631e-04 2.295693e-03 2.132351e-05
## 156 157 158 159 160
## 1.518723e-03 7.688412e-04 3.637548e-04 4.600586e-04 1.630315e-05
## 161 162 163 164 165
## 9.387885e-04 3.109898e-04 2.811556e-05 2.696406e-03 1.006388e-03
## 166 167 168 169 170
## 6.305138e-03 1.826157e-05 1.139847e-04 9.890679e-04 4.622274e-05
## 171 172 173 174 175
## 5.052888e-05 4.211214e-03 2.027140e-03 2.798842e-03 6.994851e-04
## 176 177 178 179 180
## 6.132901e-03 3.532210e-03 6.137388e-04 7.337603e-03 8.815952e-03
## 181 182 183 184 185
## 5.383469e-03 5.982091e-03 2.209876e-04 5.225183e-04 1.736916e-03
## 186 187 188 189 190
## 1.868019e-04 1.227234e-03 2.975273e-03 9.202072e-05 2.526248e-03
## 191 192 193 194 195
## 4.980183e-03 1.872972e-04 1.115488e-04 1.887004e-04 7.764134e-05
## 196 197 198 199 200
## 4.584208e-04 7.579627e-05 5.554306e-06 1.657696e-04 1.571302e-04
## 201 202 203 204 205
## 1.887963e-04 1.178353e-03 8.196134e-06 1.292070e-04 6.988422e-04
## 206 207 208 209 210
## 1.836346e-03 9.680570e-03 3.959528e-07 8.244072e-04 8.892333e-04
## 211 212 213 214 215
## 8.193632e-07 3.196681e-03 3.262213e-04 6.803670e-04 3.960848e-03
## 216 217 218 219 220
## 7.875614e-04 4.034885e-04 9.144393e-05 2.000980e-03 1.580416e-06
## 221 222 223 224 225
## 1.251735e-04 4.853038e-05 8.364939e-04 1.050282e-02 4.277987e-04
## 226 227 228 229 230
## 3.209268e-04 2.685046e-05 1.229495e-03 1.239696e-06 3.214409e-03
## 231 232 233 234 235
## 9.698840e-04 1.182820e-02 1.021546e-04 5.277873e-07 1.127162e-04
## 236 237 238 239 240
## 1.881968e-04 2.164420e-03 4.245212e-07 1.509754e-03 1.964100e-04
## 241 242 243 244 245
## 6.573517e-03 1.950828e-03 2.166570e-02 3.045035e-03 3.120855e-03
## 246 247 248 249 250
## 1.417851e-03 9.999129e-03 2.069329e-05 2.226214e-03 4.527933e-06
## 251 252 253 254 255
## 3.130802e-03 6.585050e-04 6.513967e-04 1.986348e-04 4.878517e-06
## 256 257 258 259 260
## 1.114737e-03 2.094699e-05 1.568792e-03 1.800409e-05 4.649115e-04
## 261 262 263 264 265
## 1.585284e-06 1.964130e-03 5.910648e-03 1.432358e-03 2.332845e-08
## 266 267 268 269 270
## 4.030685e-04 2.754178e-03 3.626445e-03 9.083886e-04 1.011470e-02
## 271 272 273 274 275
## 8.473261e-03 3.585344e-05 4.637712e-03 9.694950e-06 1.749809e-04
## 276 277 278 279 280
## 8.280766e-03 6.874586e-05 4.168752e-03 2.036204e-03 7.963922e-05
## 281 282 283 284 285
## 3.215642e-06 3.875906e-03 1.643751e-04 9.433776e-04 8.932770e-05
## 286 287 288 289 290
## 9.516064e-05 2.844443e-04 4.194760e-04 1.148010e-04 7.885892e-04
## 291 292 293 294 295
## 1.053573e-03 2.040621e-03 1.746390e-02 1.459593e-03 6.959472e-04
## 296 297 298 299 300
## 5.881585e-04 2.134193e-04 2.817285e-04 6.740716e-05 6.774610e-03
## 301 302 303 304 305
## 3.136208e-03 2.552473e-03 1.167534e-04 5.114699e-04 2.411268e-03
## 306 307 308 309 310
## 1.010636e-04 1.428834e-03 2.352240e-03 3.147816e-03 5.248036e-06
## 311 312 313 314 315
## 1.550405e-04 7.489822e-04 2.098045e-03 5.707228e-04 4.662413e-04
## 316 317 318 319 320
## 2.157255e-04 1.327133e-03 1.356481e-04 1.638573e-03 5.604195e-04
## 321 322 323 324 325
## 1.285783e-03 5.643174e-07 2.122820e-04 1.265711e-04 4.761796e-04
## 326 327 328 329 330
## 5.093441e-03 1.105760e-06 3.573770e-04 4.116176e-03 4.816687e-04
## 331 332 333 334 335
## 5.366328e-06 5.590812e-04 1.630920e-06 2.778076e-06 1.104570e-04
## 336 337 338 339 340
## 1.016314e-04 1.449896e-03 5.954211e-05 1.012711e-04 4.983936e-03
## 341 342 343 344 345
## 1.939200e-04 2.196996e-04 1.171223e-03 5.847426e-04 1.630944e-03
## 346 347 348 349 350
## 8.677706e-08 2.287167e-03 2.132634e-05 2.309821e-03 2.387297e-06
## 351 352 353 354 355
## 1.733529e-04 4.974783e-05 2.299280e-04 8.510232e-04 2.006994e-02
## 356 357 358 359 360
## 4.177580e-04 5.147529e-03 5.117771e-04 2.998917e-04 1.351073e-03
## 361 362 363 364 365
## 6.899045e-04 5.228499e-03 4.600990e-03 4.669527e-04 8.438978e-04
## 366 367 368 369 370
## 1.628354e-02 7.624859e-04 8.018057e-04 4.777453e-06 1.873800e-03
## 371 372 373 374 375
## 1.819473e-03 1.832969e-04 4.039127e-04 3.244130e-03 1.685125e-03
## 376 377 378 379 380
## 1.025939e-04 3.137450e-05 2.509090e-05 9.521722e-05 3.301360e-06
## 381 382 383 384 385
## 2.001649e-03 1.905834e-05 6.323092e-03 1.292753e-03 8.664254e-06
## 386 387 388 389 390
## 7.407007e-03 2.359656e-03 1.803314e-03 2.069562e-03 4.253547e-05
## 391 392 393 394 395
## 1.136323e-04 1.140534e-04 4.975520e-03 4.496540e-05 2.558134e-04
## 396 397 398 399 400
## 1.133500e-04 1.842323e-05 2.351419e-03 8.634116e-04 2.216123e-05
## 401 402 403 404 405
## 4.282417e-04 6.879309e-06 4.223486e-04 5.942391e-03 1.266087e-03
## 406 407 408 409 410
## 1.072475e-03 9.572363e-06 3.647850e-03 4.771934e-03 4.535670e-03
## 411 412 413 414 415
## 3.759026e-05 1.471750e-02 1.470953e-03 3.668430e-05 5.600332e-05
## 416 417 418 419 420
## 9.061783e-05 3.107488e-04 1.358236e-04 4.546927e-04 6.059712e-04
## 421 422
## 5.939650e-04 1.150430e-03
#Create histogram
#A density plot of the residuals
plot(density(resid(model3)))
#Create a QQ plot qqPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model3) # leverage plots
#Collinearity
vif(model3)
## ydata$toptim ydata$tmarlow ydata$tpstress ydata$gender
## 1.291821 1.075754 1.386133 1.050668
sqrt(vif(model3))
## ydata$toptim ydata$tmarlow ydata$tpstress ydata$gender
## 1.136583 1.037185 1.177342 1.025021
#Model 4 adding in interaction term gender*stress
#create interaction term
ydata$intgenstress=as.numeric(ydata$gender)*ydata$tpstress
model4=lm(ydata$tpcoiss~ydata$toptim+ydata$tmarlow+ydata$tpstress+ydata$gender+ydata$intgenstress)
summary(model4)
##
## Call:
## lm(formula = ydata$tpcoiss ~ ydata$toptim + ydata$tmarlow + ydata$tpstress +
## ydata$gender + ydata$intgenstress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.275 -5.186 0.235 5.836 28.198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.48477 4.86777 11.398 < 2e-16 ***
## ydata$toptim 0.86682 0.11318 7.659 1.33e-13 ***
## ydata$tmarlow 1.02637 0.22671 4.527 7.81e-06 ***
## ydata$tpstress -0.69471 0.23450 -2.962 0.00323 **
## ydata$genderMALES 3.42931 4.24948 0.807 0.42013
## ydata$intgenstress -0.06507 0.15766 -0.413 0.68000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9 on 416 degrees of freedom
## Multiple R-squared: 0.4451, Adjusted R-squared: 0.4385
## F-statistic: 66.75 on 5 and 416 DF, p-value: < 2.2e-16
plot(model4)
#Check assumptions
#Cooks distance
cooks.distance(model4)
## 1 2 3 4 5
## 3.683116e-04 1.178676e-02 1.644426e-02 5.921484e-04 1.911109e-03
## 6 7 8 9 10
## 3.002889e-02 1.058362e-02 3.269252e-02 1.089707e-02 2.645437e-02
## 11 12 13 14 15
## 1.950181e-02 3.899282e-02 2.062466e-04 1.560389e-02 1.749112e-04
## 16 17 18 19 20
## 2.178498e-03 4.778911e-03 2.797210e-02 6.712949e-04 7.054063e-04
## 21 22 23 24 25
## 1.207878e-04 2.932034e-02 2.164039e-03 1.732762e-03 1.776822e-03
## 26 27 28 29 30
## 8.438375e-06 5.174328e-03 1.477976e-03 1.689095e-05 6.693014e-04
## 31 32 33 34 35
## 2.870488e-02 1.367956e-03 7.293801e-05 3.527067e-04 1.119045e-03
## 36 37 38 39 40
## 3.316852e-04 7.061671e-04 4.842655e-03 1.009167e-03 5.502894e-03
## 41 42 43 44 45
## 3.682338e-04 3.127571e-03 8.421178e-03 3.146750e-03 4.488304e-04
## 46 47 48 49 50
## 6.177542e-03 2.151253e-04 1.680959e-03 6.133201e-04 4.631203e-03
## 51 52 53 54 55
## 1.001518e-01 7.167624e-02 7.277119e-04 3.383246e-03 2.016119e-03
## 56 57 58 59 60
## 2.350115e-04 5.663261e-03 7.809555e-04 1.041914e-04 5.772658e-03
## 61 62 63 64 65
## 8.643961e-03 1.290567e-02 3.897609e-05 1.109233e-03 6.436888e-03
## 66 67 68 69 70
## 8.623124e-04 3.626219e-03 7.881128e-04 8.903274e-04 7.153656e-04
## 71 72 73 74 75
## 2.233232e-04 2.984345e-08 4.815933e-04 1.510601e-02 5.630290e-06
## 76 77 78 79 80
## 1.047456e-02 1.711374e-03 2.787357e-04 7.954411e-04 2.579801e-03
## 81 82 83 84 85
## 1.089499e-04 7.386730e-04 1.983170e-04 1.420885e-03 1.129245e-03
## 86 87 88 89 90
## 1.195295e-03 2.300407e-04 5.443813e-03 6.965125e-04 9.945682e-04
## 91 92 93 94 95
## 4.931185e-05 5.330733e-06 7.924720e-04 8.064176e-03 2.843402e-04
## 96 97 98 99 100
## 2.403436e-05 7.286398e-04 1.084999e-02 4.658209e-04 7.429898e-04
## 101 102 103 104 105
## 1.828286e-03 1.203475e-03 3.675654e-04 3.681127e-04 1.756676e-03
## 106 107 108 109 110
## 1.981103e-03 9.754931e-03 2.354276e-05 3.355610e-03 1.756504e-04
## 111 112 113 114 115
## 3.399336e-06 5.491710e-04 6.431870e-06 9.923681e-03 3.236055e-03
## 116 117 118 119 120
## 1.624381e-03 1.172468e-05 2.206231e-03 1.337213e-03 8.058774e-04
## 121 122 123 124 125
## 4.108480e-03 1.170423e-02 3.615455e-03 8.760133e-06 1.472871e-06
## 126 127 128 129 130
## 1.144466e-04 9.985317e-05 4.278511e-04 1.536422e-04 1.317295e-03
## 131 132 133 134 135
## 1.372503e-03 9.001797e-04 3.873307e-04 3.479622e-02 1.093127e-02
## 136 137 138 139 140
## 1.703842e-03 5.474786e-04 1.924143e-03 3.277167e-06 2.786034e-03
## 141 142 143 144 145
## 8.920424e-06 4.944636e-03 2.807581e-03 1.324993e-04 4.125021e-05
## 146 147 148 149 150
## 1.116912e-02 6.872314e-03 2.655669e-03 1.348741e-03 5.622060e-04
## 151 152 153 154 155
## 1.801882e-03 4.300273e-06 5.199456e-04 2.348412e-03 2.588558e-05
## 156 157 158 159 160
## 1.433510e-03 7.745445e-04 3.306319e-04 4.034340e-04 1.404673e-05
## 161 162 163 164 165
## 7.893235e-04 2.621461e-04 1.683682e-05 2.722357e-03 8.687618e-04
## 166 167 168 169 170
## 6.523981e-03 1.382915e-05 1.082414e-04 1.165182e-03 3.988461e-05
## 171 172 173 174 175
## 4.140182e-05 5.271212e-03 2.711268e-03 3.018363e-03 7.328011e-04
## 176 177 178 179 180
## 5.153066e-03 3.042363e-03 5.065314e-04 6.485450e-03 1.062737e-02
## 181 182 183 184 185
## 4.907789e-03 5.088367e-03 4.011871e-04 4.368638e-04 1.502905e-03
## 186 187 188 189 190
## 2.073765e-04 1.662333e-03 2.553593e-03 7.616832e-05 2.195589e-03
## 191 192 193 194 195
## 4.695773e-03 1.739894e-04 1.441452e-04 1.828951e-04 5.316878e-05
## 196 197 198 199 200
## 4.573369e-04 1.054271e-04 8.035693e-06 1.711428e-04 1.323312e-04
## 201 202 203 204 205
## 1.627571e-04 1.017564e-03 1.343025e-05 1.048791e-04 5.848871e-04
## 206 207 208 209 210
## 1.798831e-03 8.274625e-03 7.276398e-07 6.814074e-04 7.999788e-04
## 211 212 213 214 215
## 2.636695e-06 4.196595e-03 3.326340e-04 5.668468e-04 3.560563e-03
## 216 217 218 219 220
## 7.932861e-04 5.116409e-04 8.555473e-05 1.993805e-03 2.969881e-06
## 221 222 223 224 225
## 1.038617e-04 3.587097e-05 7.723367e-04 1.043787e-02 3.632631e-04
## 226 227 228 229 230
## 2.918906e-04 2.170598e-05 1.274902e-03 1.191147e-06 2.706881e-03
## 231 232 233 234 235
## 1.002980e-03 1.127884e-02 1.462014e-04 2.341247e-06 9.691864e-05
## 236 237 238 239 240
## 1.562080e-04 1.918112e-03 1.208516e-06 1.577807e-03 2.246451e-04
## 241 242 243 244 245
## 6.856845e-03 1.643265e-03 1.836275e-02 3.000762e-03 2.938401e-03
## 246 247 248 249 250
## 1.424394e-03 1.059559e-02 1.504406e-05 1.875266e-03 3.270413e-06
## 251 252 253 254 255
## 3.020612e-03 5.479769e-04 5.347724e-04 1.788675e-04 7.067421e-06
## 256 257 258 259 260
## 1.579329e-03 1.297818e-05 1.306728e-03 1.618743e-05 4.197649e-04
## 261 262 263 264 265
## 5.603899e-07 1.682458e-03 5.078914e-03 1.249098e-03 2.138688e-07
## 266 267 268 269 270
## 3.637804e-04 2.297152e-03 3.625006e-03 9.706161e-04 8.453090e-03
## 271 272 273 274 275
## 8.221500e-03 2.903182e-05 3.917443e-03 1.289357e-05 1.876943e-04
## 276 277 278 279 280
## 7.811538e-03 6.241586e-05 3.669516e-03 2.260326e-03 9.696378e-05
## 281 282 283 284 285
## 1.075501e-05 3.439622e-03 1.476867e-04 9.451931e-04 8.043664e-05
## 286 287 288 289 290
## 8.006605e-05 2.608237e-04 3.642120e-04 1.110590e-04 6.912347e-04
## 291 292 293 294 295
## 1.037926e-03 2.302189e-03 1.506446e-02 1.213464e-03 5.784579e-04
## 296 297 298 299 300
## 5.477090e-04 2.494791e-04 2.621553e-04 5.609695e-05 6.037795e-03
## 301 302 303 304 305
## 2.623062e-03 2.190796e-03 1.184799e-04 4.595411e-04 2.136557e-03
## 306 307 308 309 310
## 1.178762e-04 1.255140e-03 1.957706e-03 2.617487e-03 4.647854e-06
## 311 312 313 314 315
## 1.203079e-04 7.784063e-04 1.996550e-03 5.339854e-04 4.768896e-04
## 316 317 318 319 320
## 1.873916e-04 1.377090e-03 1.124370e-04 1.388773e-03 7.133237e-04
## 321 322 323 324 325
## 1.068561e-03 6.688153e-07 2.277190e-04 1.005425e-04 4.126710e-04
## 326 327 328 329 330
## 4.239403e-03 3.872964e-07 3.208166e-04 3.558723e-03 3.987121e-04
## 331 332 333 334 335
## 4.336547e-07 6.265775e-04 6.362877e-07 2.184722e-06 1.503205e-04
## 336 337 338 339 340
## 8.629488e-05 1.203576e-03 5.342945e-05 8.276439e-05 4.172393e-03
## 341 342 343 344 345
## 2.010043e-04 1.813412e-04 1.103757e-03 5.116216e-04 1.421534e-03
## 346 347 348 349 350
## 3.237523e-07 2.124335e-03 1.656522e-05 2.107369e-03 1.064613e-06
## 351 352 353 354 355
## 1.406517e-04 4.036877e-05 1.898873e-04 7.213794e-04 1.674341e-02
## 356 357 358 359 360
## 3.894949e-04 5.131893e-03 4.280909e-04 2.882945e-04 1.268574e-03
## 361 362 363 364 365
## 6.128398e-04 4.653312e-03 3.966617e-03 4.178548e-04 7.446793e-04
## 366 367 368 369 370
## 1.399947e-02 7.238569e-04 6.688734e-04 8.117083e-06 1.548044e-03
## 371 372 373 374 375
## 1.528814e-03 1.666879e-04 3.347214e-04 2.698099e-03 1.396226e-03
## 376 377 378 379 380
## 9.286380e-05 2.205523e-05 2.483743e-05 9.129923e-05 3.195493e-06
## 381 382 383 384 385
## 1.689474e-03 1.323054e-05 5.653313e-03 1.081766e-03 1.099372e-05
## 386 387 388 389 390
## 6.544350e-03 2.091592e-03 1.572124e-03 1.877792e-03 3.741160e-05
## 391 392 393 394 395
## 9.321803e-05 9.272344e-05 4.160715e-03 4.927077e-05 2.306507e-04
## 396 397 398 399 400
## 9.357719e-05 2.022122e-05 1.968139e-03 7.278751e-04 2.329951e-05
## 401 402 403 404 405
## 3.854759e-04 5.634831e-06 3.591673e-04 4.942919e-03 1.053912e-03
## 406 407 408 409 410
## 9.012352e-04 9.246236e-06 3.098641e-03 3.988597e-03 3.768479e-03
## 411 412 413 414 415
## 3.350123e-05 1.248138e-02 1.320237e-03 3.436121e-05 4.610486e-05
## 416 417 418 419 420
## 7.284765e-05 2.678897e-04 1.200142e-04 3.945567e-04 5.042197e-04
## 421 422
## 5.055682e-04 9.536790e-04
#Create histogram
#A density plot of the residuals
plot(density(resid(model4)))
#Create a QQ plot qqPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model4) # leverage plots
#Collinearity
vif(model4)
## ydata$toptim ydata$tmarlow ydata$tpstress
## 1.296847 1.087557 9.791870
## ydata$gender ydata$intgenstress
## 22.979404 27.390333
sqrt(vif(model4))
## ydata$toptim ydata$tmarlow ydata$tpstress
## 1.138792 1.042860 3.129196
## ydata$gender ydata$intgenstress
## 4.793684 5.233577